It is known to purify gases with the aid of reactors having a moving layer and wherein the gas flows diagonally. In the German open application 29 11 721, for instance, a process for the removal of sulfur oxides and nitrogen oxides is disclosed, wherein the exhaust gases are passed diagonally through a reactor with a moving layer of granular, carbonaceous adsorption agents, traveling from the top to the bottom. The adsorption agent is supplied through a distribution chamber, which does not have shutters, located at the top of the reactor, to the moving layer traversed by gas, which is laterally limited by shutters through which the exhaust gas can enter, respectively exit. The adsorption agent travels slowly downwardly, into a discharge chamber, which again is not limited by shutters. The cone-shaped chamber which are filled with the adsorption agent, are not traversed by the exhaust gas. The more compact the build of the adsorber, i.e. the higher the ratio of the bed depth to the bed height, the higher becomes the ratio of the space which is not traversed by gas to the active adsorber volume.